Invariants of some abelian p-groups in characteristic p
Mara D. Neusel
Proc. Amer. Math. Soc. 125 (1997), 1921-1931.

Abstract. An explicit description of the ring of polynomial invariants of 
cyclic groups of order $p^s$ with fixed point set of codimension 2, or with 
covariants of codimension 2, over a field of characteristic $p$ is given. 
It transpires that these rings are complete intersections. A slight 
generalization for some abelian p-groups is also derived, which leads to a 
result about arbitrary groups with p-Sylow subgroup of this type.